A piezoelectric thin film resonator is used as a high frequency circuit of a cellular phone or the like. There are a film bulk acoustic resonator (FBAR) type and a solidly mounted resonator (SMR) type of piezoelectric thin film resonators. In late years, the balanced output is frequently requested at a reception terminal of an antenna duplexer. However, the filter using FBAR or SMR is not capable of converting unbalanced signals to balanced signals and the reverse. Thus, there has been developed a coupled resonator filter (CRF) structure capable of converting the unbalanced signals to the balanced signals and the reverse (for example, see non-Patent Document 1 (Improved Coupled Resonator Filter Performance using a Carbon-doped Oxide de-coupling Layer”, IEEE Ultrasonics Symp., 2009)). CRF has a plurality of piezoelectric thin film resonators and a decoupler film. The piezoelectric thin film resonators are stacked so as to interpose the decoupler film therebetween.
Non-Patent Document 2 (Advanced Materials 2009, 21, pp. 593-596) describes that the piezoelectric constant is increased by adding Sc (scandium) to aluminum nitride. Non-Patent Document 3 (Mater. Res. Soc Symp. Proc., Vol. 1129, 2009, pp. 21-25) describes that the piezoelectric constant is increased by adding Er (erbium) to aluminum nitride.
In CRF, two resonance characteristics of an anti-symmetry mode of the low frequency side and a symmetric mode of the high frequency side appear. When too large spacing between two resonance frequencies results in a loss in the vicinity of the center of the band, the loss in the vicinity of the center of the band can be suppressed by reducing the acoustic impedance of the decoupler film. However, the reduction in the acoustic impedance of the decoupler film will increase the loss resulting from the decoupler film itself.